Department of Mathematics, UC Davis
One Shields Ave.
Davis, CA 95616-8633
I am currently a Krener Assistant Professor in the Department of Mathematics at UC Davis. In Fall 2022, I was a Viterbi Endowed Postdoctoral Fellow at MSRI/SLMath, in the Fall 2022 Floer Homotopy Theory semester program. Before that, I was a Limited Term Assistant Professor in the Department of Mathematics at the University of Georgia. I received my PhD in 2019 from Boston College under the supervision of J. Elisenda Grigsby and David Treumann, and spent my fifth year as a Visiting PhD Student at Columbia University.
My research is in the field of low-dimensional topology, which for me means knots, links, and their relationships with 3- and 4-dimensional spaces, sometimes with extra geometric structure. I focus on connections between two families of homology-type invariants: quantum link homology theories and Floer theories. In particular, I construct and study analogues to algebraic constructions from Heegaard Floer homologies in Khovanov homologies, in order to explore the depths of geometric and topological information captured within quantum invariants. My exploration has led me to become interested in tools from homotopy theory, representation theory, combinatorics, symplectic/contact geometry, and more!
[CV, updated September 2022]
On Khovanov homology and related invariants
Carmen Caprau, Nicolle González, Christine Ruey Shan Lee, Adam M. Lowrance, Radmila Sazdanović, and Melissa Zhang
Proceedings Volume of the Research Collaboration Conference of the Women in Symplectic and Contact Geometry and Topology
Annular link invariants from the Sarkar-Seed-Szabó spectral sequence
Linh Truong and Melissa Zhang
Michigan Mathematical Journal
Localization in Khovanov homology
Matthew Stoffregen and Melissa Zhang
Accepted for publication in Geometry & Topology
A rank inequality for the annular Khovanov homology of 2-periodic links
Algebraic & Geometric Topology
Concordance invariants from U(1)xU(1)-equivariant Khovanov homology
Rostislav Akhmechet and Melissa Zhang
Khovanov homology and the Involutive Heegaard Floer Homology of branched double covers
Akram Alishahi, Linh Truong, and Melissa Zhang
These are provided as .txt files; change the extension to .py.
Omega Merge Split
In August 2021, I gave a series of four lectures at the Perspectives on quantum link homology theories workshop organized by Lukas Lewark and Claudius Zibrowius and hosted by the University of Regensburg.
Videos of the lectures are available on their website:
Lecture 1: Basics of annular Khovanov homology
Lecture 2: AKh and periodic links
Lecture 3: sl(2) action on AKh, annular Khovanov-Lee homology
Lecture 4: A further sampling of applications of AKh
In Fall 2022, I organized a learning seminar at SLMath called [Homotopy Types in Low-Dimensional Topology]. Click on the link to visit the webpage containing resources for this seminar.
In my teaching, my first goal is to pique students' interest in the content, so that learning becomes a means to satisfy curiosity. In the classroom, I am currently focusing on active learning techniques, and like to give my students the time to think about questions — to ask and to answer — during our class meetings. I aim to support my students as a whole persons, as I recognize that everyone has unique struggles and needs which need to be resolved for learning to occur most efficiently.
In the Winter Quarter of 2023, I am teaching MAT 108, Introduction to Abstract Mathematics. Visit the course website [here].
is also a mathematician.
My sister-in-law Nicole Wein is a theoretical computer scientist.
My sister-in-law Natasha Wein is an artist. She works wonders with resin too.
My sister-in-law² Maya Hladisova is a designer.
[3-second talk timer demo]